Spin continuity equation and definition of spin current

Abstract

For an electron, a spin-1/2 particle, the spin charge $\mathbf{s}$, a real pseudovector with constant length, could determine the spin polarization properties in quantum mechanics. Since spin density $\rho_{\mathbf{s}}$ could be expressed as the product of probability density $\rho$ and the spin charge $\mathbf{s}$, the spin continuity equation could be derived from fundamental principles of quantum mechanics and the definition of spin current arise naturally. Only in some specific conditions the conventional definition of spin current coincides with ours. The equilibrium spin currents would vanish automatically in two-dimensional electron gas with Rashba spin-orbit interaction by using our definition of spin current.